Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 7x - 8$ and $ KL = 3x + 28$ Find $JL$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {7x - 8} = {3x + 28}$ Solve for $x$ $ 4x = 36$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 7({9}) - 8$ $ KL = 3({9}) + 28$ $ JK = 63 - 8$ $ KL = 27 + 28$ $ JK = 55$ $ KL = 55$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {55} + {55}$ $ JL = 110$